# Question: Is NP Complete The Longest Path?

## Is Hamiltonian path NP-complete?

The problem is to determine if there is a simple path that crosses each vertex of the graph.

A Hamiltonian path is a simple open path that contains each vertex in a graph exactly once.

Hamiltonian Cycle is NP-complete, so we may try to reduce this problem to Hamiltonian Path..

## What does NP mean in NP-complete?

nondeterministic polynomial timeThe complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.

## How do you know if a problem is NP-complete?

A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete.

## Is NP the shortest path?

Since it is also in NP, it is NP-Complete. The shortest path on the other hand is a different one, it asks what is the shortest way from point A to point B, and it is in P because there is a polynomial time algorithm that solves it (Dijkstra’s algorithm, Bellman-Ford, BFS for non weighted graphs).

## How do you find the longest path in a dag?

We can call the DFS function from every node and traverse for all its children. The recursive formula will be: dp[node] = max(dp[node], 1 + max(dp[child1], dp[child2], dp[child3]..)) At the end check for the maximum value in dp[] array, which will be the longest path in the DAG.

## Is there any NP-complete optimization problems?

The complexity class NP only contains decisions problems per definition. So there aren’t any optimizations problems in it.

## Can Dijkstra find longest path?

The Dijkstra Algorithm is an algorithm that allows you to allocate the shortest path in a graph between a starting node i and an end note j by inlcuding other nodes of the graph. It can also be used to calculate longest paths, if some simple modifications are used.

## Does every graph have a maximal path?

This is always true: any two maximal paths will share a common vertex. We have shown that disjoint paths are not maximal, which means that any two maximal paths intersect. As shown above, the graph of a tree has two maximal paths that share no common vertex. The length of the maximal paths is 5.

## What is meant by NP-hard problem?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

## Is traveling salesman NP-complete?

Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).

## Why is longest path NP-complete?

Now it is easy to conclude that Longest Path is NP-complete because it is in NP and HamiltonianPath ∝ LongestP ath simply by observing that there is a Hamiltonian path in G if and only if there is a path of length n − 1.

## What is Dijkstra shortest path algorithm?

One algorithm for finding the shortest path from a starting node to a target node in a weighted graph is Dijkstra’s algorithm. The algorithm creates a tree of shortest paths from the starting vertex, the source, to all other points in the graph.

## What is the best shortest path algorithm?

What Is the Best Shortest Path Algorithm?Dijkstra’s Algorithm. Dijkstra’s Algorithm stands out from the rest due to its ability to find the shortest path from one node to every other node within the same graph data structure. … Bellman-Ford Algorithm. … Floyd-Warshall Algorithm. … Johnson’s Algorithm. … Final Note.Jul 13, 2020

## How do you find the longest path?

The longest simple path problem can be solved by converting G to -G (i.e. inverting the sign of the weight of each edge in the original G), and then calculate the shortest simple path.

## Is Path NP-complete?

PATH is an NP-complete problem if and only if P = NP = NP-complete. Similarly, proving that PATH isn’t an NP-complete problem would be equivalent to proving P ≠ NP ≠ NP-complete. If PATH isn’t an NP-complete problem, then no problem in P is, because all P problems are reducible to each other in polynomial time.